Universal Gravitation
Objectives
* Compare and contrast gravitational force vectors as mass and distance are changed. (Explorations 1, 2, and 3) * Discover how changes in the distance between two objects affects the gravitational force between them. (Explorations 1, 2, and 3) * Describe how changes in the masses of two objects affects the gravitational force between them. (Explorations 1, 2, and 3) Description of Activity

In this activity, you will explore how distance and mass affect the gravitational force between two objects. You will select one of three locations to work within: a 9 m2 room, a 9 × 104 m2 city block, or a 9 × 1022 m2 region of space. You will also change the mass of each object as well as manipulate the positions of both objects. For purposes of this simulation, masses will be represented as spheres and the distance between them will be the distance between their centers. Jump Start

1. What is mass? Mass is a coherent, typically large body of matter with no definite shape. 2. Describe gravitational force. The force of attraction between all masses in the universe; especially the attraction of the earth's mass for bodies near its surface; "the more remote the body the less the gravity"; "the gravitation between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them". 3. How can you tell if one variable is directly proportional to another variable? One variable is directly proportional to another if increasing/decreasing the first variable increases/decreases the second variable by the same proportion. 4. How can you tell if one variable is inversely proportional to another variable? As the first variable increases the second variable decreases or vice versa means one variable is nversely proportional to another. 5. Write Newton’s law of universal gravitation as an equation. Exploration 1: Gravitational Interactions in a Room...

...Newton’s Laws of Cooling & UniversalGravitation
Law’s of Cooling:
Newton's law of cooling is used measure the temperature change of an object of some
temperature placed in a place of a different temperature. The law states that
dT/dt= k(T-R)
where T is the temperature of the object at time t, R is the temperature of the surrounding of the
place (constant) and k is a constant of proportionality. This law states that the rate of change of
temperature is proportional to the difference between the temperature of the object and that of
the surrounding environment.
In order to get the previous equation to something that we can use, we must solve the
differential equation. The steps are given below.
1. Separate the variables. Get all the T's on one side and all the t's on the other side. The constants can be on either side.
dT/T-R = k dt
2. Anti-differentiate both sides.
Ln( T-R ) = kt - C
3. Leave in the previous form or solve for T.
T= e^kt-C + R
When working with this law, remember that t is the variable, the other letters, R, k, C, are
all constants. To find the temperature of the object at a given time, all of the constants first
should have numerical values. In some cases of convection, you could apply this law and use it
to get whatever it is you need.
Law’s of UniversalGravitation:
Isaac Newton compared the acceleration of the moon to the acceleration of objects on
earth believing...

...Assignments in Science Class IX (Term I)
10a
Gravitation
IMPORTANTIMPORTANT NOTES NOTES IMPORTANT NOTES
7. Acceleration due to gravity of the Earth : The acceleration with which the bodies fall towards the earth is called acceleration due to gravity. Its average value is 9.81 ms–2. 8. Variation of acceleration due to gravity. (i) Acceleration due to gravity changes with the change in distance from the centre of the earth. (ii) Acceleration due to gravity is maximum at the poles of the earth. Its value decreases as we move towards the equator, such that its magnitude is least at the equator. (iii) Acceleration due to gravity decreases as we move inside the earth, such as deep mines. (iv) Acceleration due to gravity decreases as we move away from the surface of the earth, such as on the mountains, in aeroplanes, in spaceships, etc. 9. Mass : The amount of matter contained in a body is called mass. It is a scalar quantity and is measured by a physical balance. It is always a constant quantity and its unit in SI system is kilogram. 10. Weight : The force with which a body is attracted towards the centre of the Earth is called weight.
O
I. VERY SHORT ANSWER QuESTIONS
YA
Assignments for summAtive Assessment
(1 Mark)
7. Why are sleepers used below the rails? [2010 (T-I)] 8. The gravitational force between two objects is F. How will the force change when the distance between them is reduced to 1/4 th? [2010 (T-I)] 9. What is meant by buoyant...

...Newton's Law of UniversalGravitation
Gravity if one of the four fundamental forces in the universe. Though
the fundamental principles of it eluded scientists until Sir Isaac Newton was
able to mathematically describe it in 1687 (Eddington 93). Gravity plays a
serious part in everyday actions as it keeps everything on the ground; without
gravity everything would be immobile unless a force was applied (then it would
move infinitely because there would be no force to stop it).
Perhaps, the best place to start then would be with such a simple item
as an apple (after all it is what "sparked" Newton's creativity). The apple is
one of the two curiosities (the other being the moon) that led Newton to
discover The Law of UniversalGravitation in 1666 (Eddington 93). As Newton
later wrote, it is the story of the sight of an apple falling to the ground (he
was resting at Woolsthorpe because of the plague at Cambridge) that caused
Newton to wonder if this same force was what held the moon in place (Gamow 41).
Newton knew that an object fell to the earth at a rate of about 9.8
meters (32 feet) per second second as pointed out by Galileo. Thus "the apple
that fell from the tree" fell to Earth at about this rate. For the first basic
explanation of this we will assume a linear plane, one in which all forces act
in only one direction. Therefore when the apple fell it went straight towards
the center of the earth...

...There is a popular story that Newton was sitting under an apple tree, an apple fell on his head, and he suddenly thought of the Universal Law of Gravitation. As in all such legends, this is almost certainly not true in its details, but the story contains elements of what actually happened.
What Really Happened with the Apple?
Probably the more correct version of the story is that Newton, upon observing an apple fall from a tree, began to think along the following lines: The apple is accelerated, since its velocity changes from zero as it is hanging on the tree and moves toward the ground. Thus, by Newton's 2nd Law there must be a force that acts on the apple to cause this acceleration. Let's call this force "gravity", and the associated acceleration the "accleration due to gravity". Then imagine the apple tree is twice as high. Again, we expect the apple to be accelerated toward the ground, so this suggests that this force that we call gravity reaches to the top of the tallest apple tree.
Sir Isaac's Most Excellent Idea
Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an...

...7.1 Newton’s Law of UniversalGravitation
Newton’s Law of UniversalGravitation states that:
Every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Consider two particles of masses m1 and m2 separated by a distance r. Each will exert a force F on the other, given by
where F : gravitational force between the two particles.
m1, m2 : masses of the two particles.
r : distance between the two particles.
G : constant of universalgravitation.
m1
m2
F
F
r
m1
m2
F
F
r
Figure 1
The two forces form an action-reaction pair and have the following characteristics,
* are equal in magnitude,
* are opposite in direction,
* act on different bodies
* are of the same type (gravitational force).
G is a universal constant called the gravitational constant (or constant of universalgravitation), which has been measured experimentally to be : G = 6.67 x 10-11 N m2 kg-2.
Important points to note about Newton’s Law of Gravitation
1. Newton’s Law of Gravitation is a universal law. It applies everywhere in the universe.
2. Attractive Nature of gravitational force: Note that the particles in this case are always attracted to each...

...Circular Motion and Gravitation
Circular motion is everywhere, from atoms to galaxies, from flagella to Ferris wheels. Two terms are frequently used to describe such motion. In general, we say that an object rotates when the axis of rotation lies within the body, and that it revolves when the axis is outside it. Thus, the Earth rotates on its axis and revolves about the Sun.
When a body rotates on its axis, all the particles of the body revolve – that is, they move in circular paths about the body’s axis of rotation. For example, the particles that make up a compact disc all travel in circles about the hub of the CD player. In fact, as a “particle” on Earth, you are continually in circular motion about the Earth’s rotational axis.
Gravity plays a large role in determining the motions of the planets, since it supplies the force necessary to maintain their nearly circular orbits. Newton’s Law of Gravity describes this fundamental force and will analyze the planetary motion in terms of this and other related basic laws. The same considerations will help you understand the motions of Earth satellites, of which there is one natural one and many artificial ones.
Angular Measure
Motion is described as a time rate of change of position. Angular velocity involves a time rate of change of position, which is expressed by an angle. It is important to be able to relate the angular description of circular motion to the orbital or tangential...

...There is no universal category of Childhood. Discuss.
To have a universal category of Childhood, all first hand and second hand experiences of Childhood must be the same to a certain degree. The term “universal” demands that all definitions and takes on the term must be the same without any equivocation. The interest in the concept of Childhood in terms of Sociology has increased massively since the 1980’s (Mayall 2002, James et al. 1998, Prout 2000, Lee 2001). Many Sociologists have analysed Childhood not only in contemporary terms but also how Childhood has been understood throughout history and across cultures. This research has led many to the conclusion that Childhood differs greatly throughout these variables and the concept has and does change. As well as interpreting Childhood Sociologically over time and cultures, one must also account for how different disciplines and literature such as Biology, Psychology and the Law define what is a Child and what constitutes Childhood. Many Sociologists therefore argue whether there is an essential definition of Childhood and indeed, if there can even be one. This has generated many debates over the question of whether there can ever be a “universal category” of childhood and as such has meant that our understanding of Childhood as a naturalized term has been altered.
“The sociology of/for childhoods has been an important development, challenging a range of...

...Some poets look from the particular to the universal to explore human experience. Discuss poems from at least two poets in relation to this statement, considering also the ways in which they achieve their effects.
Some poets reflect on the particular and the universals of the world to unveil certain aspects of human experience. Through the use of particular and universal ideas along with intensive visual and kinesthetic imagery, the reader is able to adopt the same feeling of awe at these simplistic spectacles as once felt by the poet. Harwood’s poem; ‘in the park’ uses particular and universal themes and objects to discuss post-natal depression. Similarly, Heaney’s Poem; ‘Blackberry picking’, uses particular and universal themes and objects to describe a human experience evoking greed and Lust and finally, the transience of time. Nature was also a major theme. Throughout Heany’s poem, Blackberry Picking, he describes the blossoming romance and sexual tension between the persona and the ripe blackberries.
Written in 1963, By Poet Gwen Harwood is the Stichic, ‘in the park’ which delves into the life of a mother experiencing post-natal depression. Throughout the poem it is evident that persona is discontent with her lifestyle. The paratactic form of the poem, consisting of enjambment, ‘a small balloon…but for the grace of God’, and hyphens ‘passes by-too late’ reflects her disjointedness with her...